-4sqrt{21/5}divsqrt{41/11}= eching

$$- 4 \sqrt { 2 \frac { 1 } { 5 } } \div \sqrt { 4 \frac { 1 } { 11 } } =$$

Baholash

$$-\frac{44}{15}\approx -2,933333333$$

Yechim qadamlari

10 hosil qilish uchun 2 va 5 ni ko'paytirish.

$$\frac{-4\sqrt{\frac{10+1}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

11 olish uchun 10 va 1'ni qo'shing.

$$\frac{-4\sqrt{\frac{11}{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

\sqrt{\frac{11}{5}} boʻlinmasining kvadrat ildizini \frac{\sqrt{11}}{\sqrt{5}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{-4\times \frac{\sqrt{11}}{\sqrt{5}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

\frac{\sqrt{11}}{\sqrt{5}} maxrajini \sqrt{5} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{\left(\sqrt{5}\right)^{2}}}{\sqrt{\frac{4\times 11+1}{11}}}$$

\sqrt{5} kvadrati – 5.

$$\frac{-4\times \frac{\sqrt{11}\sqrt{5}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

\sqrt{11} va \sqrt{5} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{-4\times \frac{\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

-4\times \frac{\sqrt{55}}{5} ni yagona kasrga aylantiring.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{4\times 11+1}{11}}}$$

44 hosil qilish uchun 4 va 11 ni ko'paytirish.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{44+1}{11}}}$$

45 olish uchun 44 va 1'ni qo'shing.

$$\frac{\frac{-4\sqrt{55}}{5}}{\sqrt{\frac{45}{11}}}$$

\sqrt{\frac{45}{11}} boʻlinmasining kvadrat ildizini \frac{\sqrt{45}}{\sqrt{11}} kvadrat ildizlarining boʻlinmasi sifatida qayta yozing.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{\sqrt{45}}{\sqrt{11}}}$$

Faktor: 45=3^{2}\times 5. \sqrt{3^{2}\times 5} koʻpaytmasining kvadrat ildizini \sqrt{3^{2}}\sqrt{5} kvadrat ildizlarining koʻpaytmasi sifatida qayta yozing. 3^{2} ning kvadrat ildizini chiqarish.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}}{\sqrt{11}}}$$

\frac{3\sqrt{5}}{\sqrt{11}} maxrajini \sqrt{11} orqali surat va maxrajini koʻpaytirish orqali ratsionallashtiring.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{\left(\sqrt{11}\right)^{2}}}$$

\sqrt{11} kvadrati – 11.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{5}\sqrt{11}}{11}}$$

\sqrt{5} va \sqrt{11} ni koʻpaytirish uchun kvadrat ildiz ichidagi sonlarni koʻpaytiring.

$$\frac{\frac{-4\sqrt{55}}{5}}{\frac{3\sqrt{55}}{11}}$$

\frac{-4\sqrt{55}}{5} ni \frac{3\sqrt{55}}{11} ga bo'lish \frac{-4\sqrt{55}}{5} ga k'paytirish \frac{3\sqrt{55}}{11} ga qaytarish.

$$\frac{-4\sqrt{55}\times 11}{5\times 3\sqrt{55}}$$

Surat va maxrajdagi ikkala \sqrt{55} ni qisqartiring.

$$\frac{-4\times 11}{3\times 5}$$

Surat va maxrajdagi ikkala -1 ni qisqartiring.

$$\frac{4\times 11}{-3\times 5}$$

44 hosil qilish uchun 4 va 11 ni ko'paytirish.

$$\frac{44}{-3\times 5}$$

-15 hosil qilish uchun -3 va 5 ni ko'paytirish.

$$\frac{44}{-15}$$

\frac{44}{-15} kasri manfiy belgini olib tashlash bilan -\frac{44}{15} sifatida qayta yozilishi mumkin.

$$-\frac{44}{15}$$

Omil

$$-\frac{44}{15} = -2\frac{14}{15} = -2,933333333333333$$